6 ms·

In your 35 second blurb, and the New York Times article, it seems like the point you're making is that interference is the main way that quantum computers work.

by lambda 8y ago

In your 35 second blurb, and the New York Times article, it seems like the point you're making is that interference is the main way that quantum computers work. But what makes quantum interference special over other kinds? You can get interference in sound waves, light waves, radio waves, etc. You also mention that magnitudes can be complex, but the same is true of other kinds of waves; complex numbers are used for discussing impedance in electronics. These are even relatively simple to work with; back in high school, I set up my basement as a darkroom, set up a sandbox for isolation, borrowed a laser from my physics teacher, bought a kit online with a beam splitter, mirrors, lenses, and film, and made some holograms of various objects utilizing light interference. You could set up an apparatus in which light goes through a beam splitter, reflects off mirrors to travel via different paths, and is recombined and interferes in the end to produce an interference pattern. You could probably encode a lot of information in the exact length of the different paths, perhaps in an array of mirrors which could be actuated to produce slightly different path lengths in different parts of the beam (after the beam is expanded), and use the interference to make calculations. Other than the smaller scale, and greater difficulty of working with it, what is special about quantum interference that would make it more amenable to solving problems that are NP complete than some apparatus producing similar kinds of interference with light? Also, has it been proven (or argued sufficiently convincingly) that quantum computation at scale is actually possible? I'm wondering if there could be an issue where it requires more computation to construct a quantum computer than the computation you get out, or require a non-constant number of quantum computers (with respect to the size of the problem) to actually get reliable enough results out, or something of the sort. I think this is somewhat like the questions of whether certain automata are Turing-complete (https://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_Turing_machine https://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_T...), when a sufficiently complex process is needed to encode the problem into the automata that it could be argued that the computation was not actually carried out by the automata itself (I don't actually know if that question was answered; Wikipedia references a mailing list thread that has a lot of discussion, but I haven't seen any authoritative conclusion). Given that empirically, only extremely simple quantum computers have been able to be constructed, what makes us think that there isn't some kind of tricky scaling issue like this were the additional complexity of building, running, or verifying the results of quantum computers will negate the benefits?

deleted 8y ago
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ScottAaronson 8y ago
The difference between QC and all those other examples of interference is that, in the case of QC, the interference happens in configuration space rather than ordinary 3-dimensional space. And configuration space is enormous; it has a dimension that grows exponentially with the number of particles. The number of paths that could interfere with each other to produce a given amplitude is likewise exponential (in that case, in the number of computational steps). No, of course no one has proven that it can work: presumably, the only proof that will convince everyone will be the actual construction of the machines! But in the 1990s, the theory of quantum error-correction convinced almost everyone that, as far as current physics can say, the difficulties (though staggering) seem to be ""merely"" difficulties of engineering. As I discussed in another answer, a deep reason why QC could never be scaled would be MUCH more interesting scientifically than a mere success in scaling it (which would "merely" confirm what physicists already believe). And of course, with the ongoing efforts of Google and others to demonstrate "quantum supremacy" with 50-70 qubits, we're likely to get experimental results that are relevant to your questions within the next few years.
- zackmorris 8y ago
  Out of all your replies, I THINK that this is the one that helped me grok why QC is different than somehow simulating quantum math in a classical computer. The idea of being able to tap into more than 3 dimensions sounds like something very fundamental, kind of like relativity, and a key aspect of how our universe works that at least I was never aware of (and probably a lot of other people!) Would you consider writing an in-depth article on configuration space and how it applies to QC (and possibly other research) and sharing it here on HN someday?
  - ScottAaronson 8y ago
    Pretty much any intro to QC (and in particular, any of the intros I've written, and linked to elsewhere on this thread) will make the point about Hilbert space (that's what it's called) having a dimension that grows exponentially with the number of particles in your system. This is because every possible classical configuration of the system is its own orthogonal "direction" in Hilbert space, and the full state can be an arbitrary superposition (i.e., complex linear combination) of those directions.

by lambda 8y ago

deleted 8y ago

[deleted]

ScottAaronson 8y ago

The difference between QC and all those other examples of interference is that, in the case of QC, the interference happens in configuration space rather than ordinary 3-dimensional space. And configuration space is enormous; it has a dimension that grows exponentially with the number of particles. The number of paths that could interfere with each other to produce a given amplitude is likewise exponential (in that case, in the number of computational steps). No, of course no one has proven that it can work: presumably, the only proof that will convince everyone will be the actual construction of the machines! But in the 1990s, the theory of quantum error-correction convinced almost everyone that, as far as current physics can say, the difficulties (though staggering) seem to be ""merely"" difficulties of engineering. As I discussed in another answer, a deep reason why QC could never be scaled would be MUCH more interesting scientifically than a mere success in scaling it (which would "merely" confirm what physicists already believe). And of course, with the ongoing efforts of Google and others to demonstrate "quantum supremacy" with 50-70 qubits, we're likely to get experimental results that are relevant to your questions within the next few years.

zackmorris 8y ago
Out of all your replies, I THINK that this is the one that helped me grok why QC is different than somehow simulating quantum math in a classical computer. The idea of being able to tap into more than 3 dimensions sounds like something very fundamental, kind of like relativity, and a key aspect of how our universe works that at least I was never aware of (and probably a lot of other people!) Would you consider writing an in-depth article on configuration space and how it applies to QC (and possibly other research) and sharing it here on HN someday?
- ScottAaronson 8y ago
  Pretty much any intro to QC (and in particular, any of the intros I've written, and linked to elsewhere on this thread) will make the point about Hilbert space (that's what it's called) having a dimension that grows exponentially with the number of particles in your system. This is because every possible classical configuration of the system is its own orthogonal "direction" in Hilbert space, and the full state can be an arbitrary superposition (i.e., complex linear combination) of those directions.